Theresa May has vowed to battle on to save her Brexit deal as she faced continued unrest within her Cabinet and party.

The Prime Minister insisted she would “see this through” despite the resignation of Cabinet ministers Dominic Raab and Esther McVey and calls led by influential backbencher Jacob Rees-Mogg for her to be ousted.

The difficulties faced by the Prime Minister appear set to continue, with speculation about Michael Gove’s next move after he reportedly rejected the offer of becoming Brexit secretary.

Mrs May said he was doing an “excellent job” as Environment Secretary, following reports he would only accept the post vacated by Mr Raab if he was allowed to renegotiate the deal secured by the Prime Minister with Brussels.

A resignation by such a high-profile Brexiteer would deal another major blow to Mrs May.

International Development Secretary Penny Mordaunt also has reservations about the plan and used meetings with Mrs May and Cabinet Secretary Mark Sedwill to argue that there should be a free vote in the Commons on the Brexit deal.

That would liberate her from collective responsibility, allowing her to remain in Cabinet while voting against the plan, but government sources indicated that “not a lot” changed as a result of the meetings.

At a defiant Downing Street press conference, Mrs May compared herself with her stubborn but effective cricketing hero as she told reporters: “What do you know about Geoffrey Boycott? Geoffrey Boycott stuck to it and he got the runs in the end.”

And she will continue efforts to win support for her deal, speaking directly to the public on a radio phone-in on Friday morning.

But the Prime Minister’s hopes of getting it through Parliament appear forlorn after a bruising Commons statement on Thursday exposed the scale of opposition from all parties.

In a particularly brutal intervention, Nigel Dodds, the Westminster leader of the Democratic Unionist Party upon whose 10 MPs the Prime Minister relies for a majority, said she “clearly doesn’t listen” and her deal would lead to a “vassal state with the breakup of the United Kingdom”.

Only a handful of her own MPs spoke up in favour of the plan, denounced by Labour leader Jeremy Corbyn as a “half-baked deal” which did not meet the six tests his party had set for it to get their support.

Labour waverers – who could be tempted to support the May plan to avoid a no-deal Brexit – were urged to stand firm by the grassroots Momentum movement, which launched a campaign to encourage party members to tell their MPs to vote down a deal.

Within the Tory ranks some 17 MPs have publicly stated that they have submitted letters of no confidence to Sir Graham Brady, chairman of the backbench 1922 Committee responsible for Tory leadership elections.

Mr Rees-Mogg, leader of the influential European Research Group (ERG) of Conservatives, said Mrs May had previously promised to serve as long as the Tories wanted her to.

“I think there are many people in the Conservative Party, not just in Parliament but in the country at large, who feel that her service now should come to an end,” he said.

Former minister James Duddridge suggested Sir Graham may already have received the 48 letters – from 15% of Tory MPs – required to trigger a vote because the Prime Minister would be given two days notice before a public announcement.